6.2.13. Suppose Lx = f(t), x(0) = 0, x'(0) = 0 for the input function f(t)x(t) = 2e+te¯* + (t − 2).-t-a) Find F(s), X(s), and the transfer function H(s).b) If the input is instead f(t) = sin(t) instead, find the new output x(t).= t has the output

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Answered: 6.2.13. Suppose Lx = f(t), x(0) = 0,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
6. Find the function f(x) such that f"(x)= 2x' +3x-4x+5, f(0) = 2 , and f(1)=0.
Let f and g be functions such that f(0) = 18, f '(0) = 3, f(18) = 11, f '(18) = - 5 and g(11) = - 23, g'(11) = - 11, g(18) = - 30, g'(18) = 43. Find the values of the following expressions. (i) (g o f)'(18) (ii) (f o f)'(0) ..... (i) (g o f)'(18) = (ii) (f o f)'(0) =
If z is implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x) (z-x)/(x-y) (y-x)/(x+5) (x-y)/(2-x)
Ex. 4) For F and G functions and given that: F(5)=-1,F"(5)=-3 G(5) = 4 G'(5) = 2 a) If P(x) = F(x)· G(x), then evaluate P'(5). P'(5) = F(x) b) If Q(x) = G(x) then evaluate Q'(5). Q'(5)=_
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1. Assume that the function is a one-to-one function. (a) If f(2) = 5, find f-'(5). Your answer is (b) If ƒ -'(– 8) : 5, find f( – 5). Your answer is 2. If f is one-to-one and f(13) = 9, then f-'(9) : - 1 and (f(13)) 3. Use the table below to fill in the missing values. f(x) 1 3 2 8 7 4 2 6 4 7 9. 6 9 f(7) = if f(x) = 2 then z = f(9) = if f-(x) = 5 then a = 4. (a) Find the inverse function of f(x) = 9x – 7. f-'(x) (b) The graphs of f and f 1 are symmetric with respect to the line defined by y =

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6.2.13. Suppose Lx = f(t), x(0) = 0, x'(0) = 0 for the input function f(t) x(t) = 2e+te¯* + (t − 2). -t - a) Find F(s), X(s), and the transfer function H(s). b) If the input is instead f(t) = sin(t) instead, find the new output x(t). = t has the output